Test method for TSpline5
n number of data points.
m 2*m-1 is order of spline.
m = 2 always for third spline.
nn,nm1,mm,
mm1,i,k,
j,jj temporary integer variables.
z,p temporary double precision variables.
x[n] the sequence of knots.
y[n] the prescribed function values at the knots.
a[200][4] two dimensional array whose columns are
the computed spline coefficients
diff[3] maximum values of differences of values and
derivatives to right and left of knots.
com[3] maximum values of coefficients.
test of TSpline3 with nonequidistant knots and
equidistant knots follows.

subroutine cubspl ( tau, c, n, ibcbeg, ibcend )
from * a practical guide to splines * by c. de boor
************************ input ***************************
n = number of data points. assumed to be .ge. 2.
(tau(i), c(1,i), i=1,...,n) = abscissae and ordinates of the
data points. tau is assumed to be strictly increasing.
ibcbeg, ibcend = boundary condition indicators, and
c(2,1), c(2,n) = boundary condition information. specifically,
ibcbeg = 0 means no boundary condition at tau(1) is given.
in this case, the not-a-knot condition is used, i.e. the
jump in the third derivative across tau(2) is forced to
zero, thus the first and the second cubic polynomial pieces
are made to coincide.)
ibcbeg = 1 means that the slope at tau(1) is made to equal
c(2,1), supplied by input.
ibcbeg = 2 means that the second derivative at tau(1) is
made to equal c(2,1), supplied by input.
ibcend = 0, 1, or 2 has analogous meaning concerning the
boundary condition at tau(n), with the additional infor-
mation taken from c(2,n).
*********************** output **************************
c(j,i), j=1,...,4; i=1,...,l (= n-1) = the polynomial coefficients
of the cubic interpolating spline with interior knots (or
joints) tau(2), ..., tau(n-1). precisely, in the interval
(tau(i), tau(i+1)), the spline f is given by
f(x) = c(1,i)+h*(c(2,i)+h*(c(3,i)+h*c(4,i)/3.)/2.)
where h = x - tau(i). the function program *ppvalu* may be
used to evaluate f or its derivatives from tau,c, l = n-1,
and k=4.

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